This invention relates to handles and escutcheons for water control valves. Such valves are used, for example, for controlling the flow rate and temperature of a shower, tub, or the like. The escutcheon is a plate that covers an opening in a wall through which the valves extend. The escutcheon and handles typically have a decorative appearance, both as to shape and finish. It is desirable to coordinate the decorative appearance of the escutcheon and handles, not only with each other but with other fixtures such as faucets, shower heads, tub spouts, drain covers, towel bars, towel racks, soap dishes, tissue holders and toothbrush holders. Furthermore, it is preferable to be able to coordinate and/or change the decorative appearance of these items without having to alter or replace the functional components underlying the decorative exteriors. Given these concerns regarding aesthetics, the further desirability of mounting the handles and escutcheon without the use of exposed or visible fasteners will be understandable. At the same time, the handle must provide a predictable, repeatable tactile response without wobble or play to convey a sense of quality. In other words, it has to feel right to the user. The need for replaceable decorative elements without visible fasteners significantly complicates the design of the handles and escutcheons. U.S. Pat. No. 5,257,645 assigned to the present assignee addresses some of these issues. The present invention is an extension of that work.